The phrase "a setback on a" is correct and usable in written English.
It can be used when discussing an obstacle or difficulty encountered in a process or project.
Example: "The team experienced a setback on a crucial phase of the project, delaying the overall timeline."
Alternatives: "a hurdle in a" or "an obstacle in a".
Then the company suffered a setback on a drug it was developing to treat Alzheimer's disease.
"The word 'tragedy' is often used to describe a setback on a sporting field but this is a real tragedy," he said.
Most recently, Mr. Ratner suffered a setback on a petition seeking a writ of habeas corpus on behalf of two British and Australian detainees, alleged members of Al Qaeda, being held at Camp X-ray, at Guantánamo Bay in Cuba.
The Tiananmen Square massacre in 1989 scared away a lot of investors, but Cheng figured it was just a setback on an irreversible journey toward economic liberalization.
But the Republicans had a setback on Friday when a federal judge reversed a new state law that halted early voting on the weekend before Election Day.
Mugabe suffered a setback on Monday when a member of the opposition won the speaker's chair in a secret ballot.
New York University's plan to re-enter the engineering field by taking over a Brooklyn engineering school suffered a setback on Thursday, after a state senator said he would investigate the merger.
Gov. Rick Scott's plan to expand Medicaid coverage to one million more people suffered a setback on Monday when a State House committee rejected it and a State Senate panel postponed considering it.
Barnes & Noble sustained a setback on Monday when a powerful proxy advisory company endorsed directors proposed by the billionaire investor Ronald W. Burkle over the company's own slate, which included its chairman, Leonard S. Riggio.
WASHINGTON — A federal judge dealt a setback on Friday to the Obama administration's crackdown on the leaking of government secrets to journalists, sharply limiting what prosecutors can ask the author of a book about the C.I.A. in court.
MOSCOW — The slow but steady gain of beer over vodka as the drink of choice among Russians suffered a setback on Wednesday when President Dmitri A. Medvedev signed a law restricting beer sales outdoors and late at night.
